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Show that f'(a) = g(a) ?

  • Thread starter jkristia
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  • #1
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Homework Statement



Problem:
1C-2 Let f(x) = (x - a)g(x). Use the definition of the derivative to calculate that f'(a) = g(a), assuming that g is continuous



Homework Equations





The Attempt at a Solution



I just started a self study of calculus using Khan and MIT OpenCourse. I am bit stuck, or maybe confused, with this exercise from MIT 18.01

The definition for the derivative is
[itex]\frac{Δy}{Δx}[/itex]=[itex]\frac{f(x)-f(a)}{x-a}[/itex]

I can replace f(x) with (x-a)g(x), but I don't know what to do with f(a). In the given solution f(a) somehow becomes 0, but I can't see how.

The given solution:
attachment.php?attachmentid=47038&stc=1&d=1336362033.png


Any help is much appreciated.
 

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  • #2
LCKurtz
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f(a) = (a-a)g(a) = 0.
 
  • #3
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ah - of course. Thank you very much
 

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